{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian Data Analysis, 3rd ed\n",
    "##  Chapter 3, demo 6\n",
    "\n",
    "Illustrate posterior inference for Bioassay data (BDA3 p. 74-)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Instructions for exercise (3.11 in BDA3)\n",
    "- Check that the range and spacing of A and B are sensible for the \n",
    "  alternative prior\n",
    "- Compute the log-posterior in a grid\n",
    "- Scale the log-posterior by subtracting its maximum value before\n",
    "  exponentiating (think why this is useful)\n",
    "- Exponentiate\n",
    "- Normalize the posterior\n",
    "- Use 2D grid sampling \n",
    "- In addition to the plots, report p(beta>0|x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.special import expit  # aka logistic\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, sys\n",
    "# add utilities directory to path\n",
    "util_path = os.path.abspath(os.path.join(os.path.pardir, 'utilities_and_data'))\n",
    "if util_path not in sys.path and os.path.exists(util_path):\n",
    "    sys.path.insert(0, util_path)\n",
    "\n",
    "# import from utilities\n",
    "import plot_tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# edit default plot settings\n",
    "plt.rc('font', size=12)\n",
    "# apply custom background plotting style\n",
    "plt.style.use(plot_tools.custom_styles['gray_background'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# seed a random state\n",
    "rng = np.random.RandomState(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# data\n",
    "x = np.array([-0.86, -0.30, -0.05, 0.73])\n",
    "n = np.array([5, 5, 5, 5])\n",
    "y = np.array([0, 1, 3, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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zJF3W7vWYdZOLipmZJeOiYmZmybiomNWRtI2kz0q6L398tuEWq2dI+ks+7fh8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\nLipmZpbM/wdXY4uua7rUzQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7df3e69fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the data\n",
    "plt.scatter(x, y/n, 50, color='C1')\n",
    "plt.xlim((-1, 1))\n",
    "plt.xlabel('log dose')\n",
    "plt.ylabel('proportion of deaths');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# compute the posterior density in grid\n",
    "#  - usually should be computed in logarithms!\n",
    "#  - with alternative prior, check that range and spacing of A and B\n",
    "#    are sensible\n",
    "A = np.linspace(-4, 8, 100)\n",
    "B = np.linspace(-10, 40, 100)\n",
    "ilogit_abx = 1 / (np.exp(-(A[:,None] + B[:,None,None] * x)) + 1)\n",
    "p = np.prod(ilogit_abx**y * (1 - ilogit_abx)**(n - y), axis=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following demonstrates an alternative \"bad\" way of calcuting the posterior density p in a for loop. The vectorised statement above is numerically more efficient. In this small example however, it would not matter that much.\n",
    "\n",
    "```python\n",
    "p = np.empty((len(B),len(A))) # allocate space\n",
    "for i in range(len(A)):\n",
    "    for j in range(len(B)):\n",
    "        ilogit_abx_ij = (1 / (np.exp(-(A[i] + B[j] * x)) + 1))\n",
    "        p[j,i] = np.prod(ilogit_abx_ij**y * ilogit_abx_ij**(n - y))\n",
    "```\n",
    "\n",
    "N.B. the vectorised expression could be made even more efficient, e.g. by optimising memory usage with in-place statements. However, it would result in a less readable code and it is not necessary here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# sample from the grid\n",
    "nsamp = 1000\n",
    "samp_indices = np.unravel_index(\n",
    "    rng.choice(p.size, size=nsamp, p=p.ravel()/np.sum(p)),\n",
    "    p.shape\n",
    ")\n",
    "samp_A = A[samp_indices[1]]\n",
    "samp_B = B[samp_indices[0]]\n",
    "# add random jitter, see BDA3 p. 76\n",
    "samp_A += (rng.rand(nsamp) - 0.5) * (A[1]-A[0])\n",
    "samp_B += (rng.rand(nsamp) - 0.5) * (B[1]-B[0])\n",
    "\n",
    "# samples of LD50 conditional beta > 0\n",
    "bpi = samp_B > 0\n",
    "samp_ld50 = -samp_A[bpi]/samp_B[bpi]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dtbKyxHPuuBWEv6PlRqPFUAA8yP6OF0TJt7TodMYuWnH2dxT+TodSV25Ih7k3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\nJuqlGudl6/uq1scBUzeJ+85vO24VG8+X9uU28PCxctH5OPj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rAIYAXAzgauTe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7df1df73c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create figure\n",
    "fig, axes = plt.subplots(2, 1, figsize=(7, 8), sharex=True)\n",
    "\n",
    "# plot the posterior density\n",
    "ax = axes[0]\n",
    "ax.imshow(p, origin='lower', aspect='auto', extent=(A[0], A[-1], B[0], B[-1]))\n",
    "ax.set_xlim([-2,8])\n",
    "ax.set_ylim([-2,40])\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "ax.grid('off')\n",
    "ax.set_title('posterior density')\n",
    "\n",
    "# plot the samples\n",
    "ax = axes[1]\n",
    "ax.scatter(samp_A, samp_B, 10, linewidth=0)\n",
    "ax.set_xlim([-2,8])\n",
    "ax.set_ylim([-2,40])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "ax.set_title('samples')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ACxwHfu1mb+B5HrVa7cds5t0lHo/LPd3l7uT9vHZxEaUdhuJqVRuqlsPJyQKH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lCsFhlkJkRvCjVhNwJjCNay9xkJNPV6REL0QY9cNJamdp9htestVW2sK2/lpycNjZipXNuq2/jL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\ntpmZWQW4YJuZmVXA/wBBVZxXideVQgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7df1d96be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot samples with the data\n",
    "xt = np.linspace(-1, 1)\n",
    "fs = expit(samp_A[:, None] + samp_B[:, None]*xt)\n",
    "\n",
    "# ceate figure\n",
    "fig, axes = plt.subplots(2, 1, figsize=(7, 8), sharex=True)\n",
    "\n",
    "# plot 10 first samples\n",
    "ax = axes[0]\n",
    "ax.plot(xt, fs[:10].T, color='C0', alpha=0.5)\n",
    "ax.scatter(x, y/n, 50, color='C1')\n",
    "ax.set_xlim((-1, 1))\n",
    "ax.set_ylabel('proportion of deaths')\n",
    "\n",
    "# plot mean and [5% 95%] interval\n",
    "ax = axes[1]\n",
    "ax.plot(xt, np.mean(fs, axis=0).T, color='C0')\n",
    "ax.plot(\n",
    "    xt,\n",
    "    np.percentile(fs, [5, 95], axis=0).T,\n",
    "    color='C0',\n",
    "    linestyle='--'\n",
    ")\n",
    "ax.scatter(x, y/n, 50, color='C1')\n",
    "ax.set_xlim((-1, 1))\n",
    "ax.set_xlabel('log dose')\n",
    "ax.set_ylabel('proportion of deaths')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7df3e945f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the histogram of LD50\n",
    "plt.hist(samp_ld50, np.arange(-0.5, 0.51, 0.02))\n",
    "plt.xlim([-0.5, 0.5])\n",
    "plt.xlabel(r'LD50 = -$\\alpha/\\beta$')\n",
    "plt.yticks(());"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
